A wealth of structural information is being accumulated from X-ray crystallography and 2D NMR spectroscopy of proteins and protein ligands. Because biological activity depends on molecular shape, it is important to compare shapes and conformations of proteins and drugs objectively and accurately. For a method to be objective, it must produce the same results in different hands. This is not the case for interactive superposition of two structures on a color computer graphics screen. It is therefore necessary to develop automatic computer algorithms for molecular comparison. A successful algorithm must (i) avoid designating dissimilar structures as similar, and (ii) vice versa. This proposal presents a protein conformation comparison method that accomplishes the first objective by taking into account the topology, not just the geometry, of protein conformations. A small molecule comparison algorithm accomplishes the second objective by using maximization of overlap of chemical volume to identify structures with similar shapes and similarly placed functional groups, even when the underlying chemical structure is quite different. A third project will develop an automatic algorithm for identifying protein binding pockets and for docking small molecules, such as drugs and hormones, into them. All three projects will be inter-disciplinary and will be based on applying differential geometry, computer science and computer graphics to studying the conformations, chemistry and interactions of proteins and drugs. The protein conformation comparison method will compute a path in molecular conformational space that connects two given conformations of a protein, or of two closely related proteins. This will help in the understanding of protein conformational transitions and structural changes due to site-specific mutagenesis experiments or natural evolution and variation, including point mutation diseases. The small molecule comparison method should help in rational drug design.